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| Mirrors > Home > ILE Home > Th. List > sseqtrrd | Unicode version | ||
| Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.) |
| Ref | Expression |
|---|---|
| sseqtrrd.1 |
|
| sseqtrrd.2 |
|
| Ref | Expression |
|---|---|
| sseqtrrd |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseqtrrd.1 |
. 2
| |
| 2 | sseqtrrd.2 |
. . 3
| |
| 3 | 2 | eqcomd 2210 |
. 2
|
| 4 | 1, 3 | sseqtrd 3230 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-11 1528 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-nf 1483 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-in 3171 df-ss 3178 |
| This theorem is referenced by: sseqtrrid 3243 fnfvima 5818 tfrlemiubacc 6415 tfr1onlemubacc 6431 tfrcllemubacc 6444 rdgivallem 6466 nnnninf 7227 nninfwlpoimlemg 7276 ccatass 11062 dfphi2 12513 ctinf 12772 imasaddfnlemg 13117 imasaddvallemg 13118 subsubm 13286 subsubg 13504 subsubrng 13947 subsubrg 13978 lidlss 14209 toponss 14469 ssntr 14565 iscnp3 14646 cnprcl2k 14649 tgcn 14651 tgcnp 14652 ssidcn 14653 cncnp 14673 txcnp 14714 imasnopn 14742 hmeontr 14756 blssec 14881 blssopn 14928 xmettx 14953 metcnp 14955 plyaddlem1 15190 plymullem1 15191 plycoeid3 15200 nnsf 15904 nninfsellemsuc 15911 |
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